Sample Periods and Descriptive Statistics

This sub-section aims to explain how the data sample is split into sub-periods to prepare it for the analysis. As previously mentioned, the dataset used in the thesis consists of spot and futures prices of Nordic power from 2005 to 2018. The reason for the length of the dataset is that a new market structure was introduced in 2003 (Nasdaq OMX, 2003). Blocks contracts were replaced with monthly contracts and seasons contracts were replaced with quarterly contracts (Nasdaq OMX, 2003). In 2005, Nasdaq started calculating the settlement price for each trading day and quoting each contract in Euro (Nasdaq OMX, n.d.). As a result of this, excluding the years before 2005 will make the dataset consistent in terms of contract lengths of the futures, and ensure the availability of a Euro-denominated settlement price for each trading day.

Table 1 - An overview of the sub-periods in the full sample

Period Date Events during sub-periods

Sub-period 1 12/01/05 – 02/24/09 Futures contracts quoted in Euro Introduction of the Settlement price

EU ETS regulation is implemented (European Union, n.d.) Sub-period 2 03/03/09 – 05/25/12 Norway joins the Elbas intraday market

Implementation of a negative price floor in the Elspot market Sub-period 3 06/04/12 – 08/28/15 Bidding area and Elbas introduced in Lithuania and Latvia

Introduction of a new web-based marketplace

Sub-period 4 09/04/15 – 11/21/18 Nord Pool appointed NEMO (Nominated Electricity Market Operator) The transition of liquidity from forward to futures contracts

The dataset is split into four sub-periods to improve the robustness of the analysis and to check if the results vary depending on different market situations, which is related to the second sub-question of the thesis. To be able to observe tendencies and thoroughly compare the obtained results, each sub-period contains equally many weekly observations, which is in accordance with previous studies on the field (Bystrom, 2003; Zanotti et al., 2009; Hanly et al., 2017). The dates listed in Table 1 are the ending dates

35 of the weeks used for the weekly returns in the time series, and the dataset ends at 11/21/2018 for both contract lengths to be able to compare the futures prices with the spot price on the same day.

Sub-periods 1-3 function as the in-sample estimation period, while sub-period 4 function as the out-of-sample evaluation period in the thesis. The analysis for sub-period 4 will be among the first studies examining this period. An illustration of how the data sample is split between an in-sample estimation period and an out-of-sample forecast evaluation period can be seen in Figure 7.

Figure 7 - Presentation of how the data is split into an in-sample estimation period and an out-of-sample forecast evaluation period

Sub-period 1 starts right after the implementation of the EU ETS regulations and the introduction of Euro quoting and settlement price calculation of the contracts (Nord Pool, n.d.-g). Sub-period 2 starts 163 weeks after the beginning of sub-period 1, and an important event in this period was that Norway joined the Elbas market, which could make the intraday market less volatile due to the characteristics of the Norwegian electricity market where most of the electricity stems from hydropower production. Another event in this period was the implementation of a negative price floor in the Elspot market (Nord Pool, n.d.-g). Both events could affect the volume traded during this period, and hence also the prices. During sub-period 3, Elbas was introduced in Lithuania and Latvia, and a new web-based marketplace was set up (Nord Pool, n.d.-g). The new web structure could make it easier for new traders to enter the market and hence lead to more market participants. At the beginning of sub-period 4, Nord Pool was appointed NEMO, and the liquidity in the market was switched from forward to futures contracts (Skjevrak, 2019).

The reason for this change was that Nasdaq wanted to attract more traders into the market (Skjevrak, 2019). General descriptive statistics of the return series are given in Table 2 and the price series are displayed graphically in Figure 8.

36 Table 2 - Descriptive statistics of weekly returns for all return series

Period Series Mean

(%)

Std. dev.

(%)

Skewness Kurtosis JB statistic Corr.

Full period

Spot 0.06 19.28 -0.13 15.68 4367.34*** -

Monthly -0.32 7.20 -0.06 3.01 0.46 0.35

Quarterly -0.16 5.72 -0.34 2.18 30.63*** 0.26

Sub-period 1

Spot 0.04 12.81 0.41 2.05 42.60*** -

Monthly -1.07 8.59 -0.07 0.97 112.62*** 0.42

Quarterly -0.78 7.22 -0.41 0.76 154.83*** 0.33

Sub-period 2

Spot -0.23 22.48 1.11 16.65 5198.19*** -

Monthly -0.26 6.96 0.44 1.31 98.69*** 0.48

Quarterly 0.02 5.50 0.53 0.53 196.34*** 0.40

Sub-period 3

Spot -0.25 18.51 0.01 4.90 98.26*** -

Monthly -0.90 7.20 -0.20 8.38 789.58*** 0.34

Quarterly -0.66 4.55 -1.39 10.85 1886.91*** 0.22

Sub-period 4

Spot 0.70 21.92 -1.65 16.94 5577.25*** -

Monthly 0.94 5.66 -0.02 0.04 16.94*** 0.20

Quarterly 0.79 5.16 -0.16 0.27 205.36*** 0.15

The Jarque-Bera (JB) statistic measures normality of the return series and asymptotically follows a chi-squared distribution with two degrees of freedom (Brooks, 2008 p. 163). The critical values for the test are 4.61 (10%), 5.99 (%), and 9.21 (1%). *, ** and *** indicate rejection of the null hypothesis at the 10%, 5%, and 1% significance level, respectively. The correlation coefficients are between both futures return series and the spot return series in the same period.

Figure 8 – Historical spot, monthly and quarterly futures prices 0

20 40 60 80 100 120 140

2005 2007 2008 2010 2011 2012 2014 2015 2016 2018

EUR/MWh

Spot Quarterly Month

37 From Table 2, weekly mean returns show a history of being very low or negative in all sub-periods except sub-period 4. Since the historical low electricity price of 6.23 EUR/MWh in the middle of 2015, the general trend has been steadily increasing electricity prices up to the end of the sample, which results in a high mean return in sub-period 4 for all series.

The standard deviation of a traded asset’s logarithmic returns is a common way in finance to describe the volatility of an asset as it measures the deviations from the expected return (Brooks, 2008, p. 383;

Bodie et al., 2011, p. 132). Examining the standard deviations of the spot returns in the different sub-periods can be helpful to infer if the performance of the hedging models depends on the spot market volatility. From Table 2, it can be inferred that the spot market is more volatile than the futures market.

This is intuitive as the delivery period for the spot prices are for the following day, whereas the futures contracts have delivery periods of one or three months and hence react less to shocks in the market, which is visible in Figure 8. Additionally, the monthly futures returns display slightly higher volatility than the quarterly futures returns, probably due to the same reasons. The results also show that the electricity spot and futures series are much more volatile than other assets, such as crude oil or equities that typically have standard deviations of about 5% and 2.5%, respectively (Hanly et al., 2017). Moreover, it can also be seen that the volatility is changing over time. As an example, the standard deviation for the spot series is only 12.81% in sub-period 1, while it is as high as 22.48% in the period after. This phenomenon will be further discussed in sub-section 6.2.3, which motivates the use of time-varying hedging models.

The distributions’ skewness measures “how much a distribution deviates from symmetry” (Stock &

Watson, 2015, p. 69). About half of the series have a skewness between -0.5 and 0.5 and are said to be approximately symmetrical (Jani, 2014, p. 114). Distributions with skewness less than -1 or higher than 1 are said to be highly skewed (Jani, 2014, p. 114), which applies for approximately one fourth of the series in the dataset. The last fourth is in the range [-1, -0.5] and [0.5, 1], and is considered to be moderately skewed (Jani, 2014, p. 114). The skewness of the distributions are in other words varying a lot across the different series.

38 The kurtosis of a distribution measures “how much mass is in its tails” (Stock & Watson, 2015, p. 71), but it is also a measure of how peaked the distribution is around its mean (Brooks, 2008, p. 162). For the return series examined, the kurtoses are mostly above 3. This indicates a leptokurtic distribution, meaning that it has fatter tails and is more peaked around the mean than a normal distribution, which is commonly found in financial time series (Brooks, 2008, p. 162). Five of the series display a kurtosis of less than 3, which indicates a platykurtic distribution with thinner tails and lesser peak around the mean compared to a normal distribution (Brooks, 2008, p. 162). The high and varying skewness and kurtosis of the return data examined are common characteristics for energy time series (Hanly et al., 2017).

The Jarque-Bera test statistic measures whether the series have a normal distribution and is given by:

𝐽𝐽𝐽𝐽=𝑛𝑛 �skewness²

6 +(kurtosis−3)²

24 � (5)

where 𝑛𝑛 denotes the number of observations (Jarque & Bera, 1980). The null hypothesis of the test is that the series has a normal distribution, and it is rejected at the 1% level of significance in all periods and for all return series, except for the monthly contract in the full period. As a result, the series cannot be confirmed to be normally distributed. This is common for general financial asset returns and also said to be a stylized fact for electricity markets (Chevallier, 2010).

The correlation between the spot returns and the monthly futures returns are higher than for the quarterly futures returns for all series analyzed. This makes intuitive sense as it is plausible that contracts with shorter delivery periods capture more of the current fundamental market information than contracts with longer delivery periods. These results give reason to expect higher hedging effectiveness from hedging with monthly futures compared to quarterly futures. The reason for this is that the idea of hedging is to offset the risk of adverse price changes by a similar price change in the hedging instrument, in which an opposite position is taken. To what extent a price reaction in the spot market is causing a price change in the hedging instrument is measured by the correlation coefficient and is hence a determinant of hedging performance (Charnes & Koch, 2003).

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